Ismail (1986) gives asymptotic expansions as n→∞, with x
and other parameters fixed, for continuous q-ultraspherical, big and little
q-Jacobi, and Askey–Wilson polynomials. These asymptotic expansions are in
fact convergent expansions. For Askey–Wilson
pn⁡(cos⁡θ;a,b,c,d|q) the leading term is given by